Find the principal values of the following
(i) `sin^(-1) (sin 1)`
(ii) `sin^(-1) (sin 2)`
(iii) `sin^(-1) (sin 10)`
(iv) `sin^(-1) (sin 20)`
(v) `sin^(-1) (sin 100)`
(vi) `sin^(-1) (sin. (29 pi)/(5))`

Explanation

To find the principal values of the given expressions, we will use the properties of the sine function and the inverse sine function. The principal value of `sin^(-1)(x)` is defined to be in the range of \([- \frac{\pi}{2}, \frac{\pi}{2}]\).

Let's solve each part step by step:

### (i) Find `sin^(-1)(sin 1)`

1. Since \(1\) is within the range of \([- \frac{\pi}{2}, \frac{\pi}{2}]\), we can directly use the property of inverse sine:
\[
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